BBP-type formulas -- an elementary approach

We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in $\mathtt{\text{sage}}$. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for $\sqrt{3}\pi$. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases but with integer coefficients. As an example of this, searching in various Pisot bases, we have discovered a formula for $\pi$ in base $1+\sqrt{3}$, along with additional formulas.